PUNK-SKA is one of the strangest yet most appealing hybrids in music, and Boston’s Mighty Mighty Bosstones is among its best purveyors.

Just back from its summer tour of Europe, the large, nattily dressed eight-man band hit Irving Plaza Monday for a top set that was aimed at fan-pleasing.

The party atmosphere, where it seems anything can happen, has never been adequately captured on the band’s studio discs – even the live records are sedate in comparison to the raucous performance these guys mount on stage.

Frontman Dicky Barrett has one speed: fast. He is sometimes able to enunciate the words to the music so they are understandable, but during most of this New York show – which started after 11 p.m. – he raged in punk glory with growls so deep in his baritone, the words were indiscernible.

It didn’t matter. The audience, predominantly college-age kids, filled in any of the lyric gaps by singing along with the necessary velocity to keep up.

The audience skanked and moshed to music that worked Barrett up to a boil, compelling him to take a stage dive onto the front rows near the show’s end.

His landing was rough – mostly because the kids didn’t expect the beefy singer to land on them.

Not so clumsy was the Bosstones’ tour manager and resident dancer, Ben Carr.

He did the Boogaloo, the Watusi, the Mashed Potato and a strange step of his own invention.

Some might ask what this guy does for the band, but you couldn’t help but be a little impressed and a lot entertained.

The Bosstones deliver a very together sound. When the group played the 1991 hit, “Where’d You Go,” and then the flip side to that song, “You Gotta Go” (from the most recent disc), there was sonic unity, albeit little musical evolution.

Why evolve when you have such an enticing sound?

As the show progressed, one couldn’t help but wonder how brass-blasting Jamaican ska was first welded to guitar-fueled punk, but some mysteries are better left unanswered.

Do you really need to know how the unlikely combination of peanut butter and jelly came about?